Systems and methods herein generally relate to the problem of voltage collapse in the context of static stability of power networks in electric utilities, and more particularly to methods for both off-line analysis and real-time monitoring of the proximity of the system to voltage collapse.
Such methods provide measures of the distance to voltage collapse, either qualitatively or quantitatively, through numerical indicators or graphical tools, in order to enable a quick diagnostic on the static stability of the network. Some methods, such as the ones disclosed herein, also provide ways to identify the particular nodes in the network that are more directly involved in the stability problems, which is of great importance when managing very large networks.
The present disclosure is framed under the general field of static stability in Electrical Power Distribution Systems. This field includes, but is not limited to, static voltage stability. The Holomorphic Embedding Load-flow Method (HELM) described in U.S. Pat. Nos. 7,519,506 and 7,979,239 provides a solution under the form of an algebraic curve enabling the study of these general static stability aspects. The most thoroughly studied problem in this field is that of voltage stability.
The problems related to voltage stability in power systems are one of the major concerns in planning and operation of large electrical power network grids. As defined by the Institute of Electrical and Electronics Engineers (IEEE) and the Council on Large Electric Systems (CIGRE), voltage stability refers to the ability of a power system to maintain steady voltages at all buses in the system after being subjected to a disturbance from a given initial operating condition. Although voltage instability may be originated by local phenomena, its consequences may have widespread impact. A typical outcome of voltage instability is loss of load in an area, or tripping of transmission lines and other elements by their protections leading to cascading outages that in turn may lead to loss of synchronism of some generators. The term “voltage collapse” is also often used: voltage collapse is the process by which the sequence of events accompanying voltage instability leads to a partial or extensive blackout in the network. Due to economical and environmental constraints, power networks have become more complex and heavily loaded. Voltage instability is then an increasingly serious problem, as utilities are pushed to operate the system closer to its limits.
According to the time frame characterizing the phenomenon of voltage stability, the IEEE/CIGRE considers short-term and long-term problems. While short-term voltage stability studies need dynamic modeling of loads (it is similar in this respect to rotor angle stability), long-term voltage stability can be assessed through several static analysis techniques. The methods disclosed herein fall within this second class of methods. In general, these techniques are based on the steady state of the system, the so-called load flow equations. The pragmatic goal is to estimate stability margins (distance to collapse), as well as identify weak nodes (those whose voltage variations are highly sensitive to further variations of load or generation in the system) in the system or other factors influencing stability.
Many static techniques have been developed to provide an estimation of the proximity to collapse. The classical technique is the use of P-V/Q-V curves, which provide a measure of the load margins. Other methods take into account the structure of the load flow problem and attempt to measure the distance to the closest bifurcation, since voltage collapse takes place when the stable load flow solution merges with an unstable one. The V/V0 index system relies on comparing the original load flow case with one in which all the loads are set to zero, in order to spot the weaker nodes. Most other systems rely on approximating the power system via the use of a local model, normally a two-bus system that can be solved exactly in closed form.